Quantum vortex reconnections

We study reconnections of quantum vortices by numerically solving the governing Gross-Pitaevskii equation. We find that the minimum distance between vortices scales differently with time before and after the vortex reconnection. We also compute vortex reconnections using the Biot-Savart law for vortex filaments of infinitesimal thickness, and find that, in this model, reconnection are time-symmetric. We argue that the likely cause of the difference between the Gross-Pitaevskii model and the Biot-Savart model is the intense rarefaction wave which is radiated away from a Gross-Pitaeveskii reconnection. Finally we compare our results to experimental observations in superfluid helium, and discuss the different length scales probed by the two models and by experiments.Comment: 23 Pages, 12 Figure

Vortex reconnections in atomic condensates at finite temperature

The study of vortex reconnections is an essential ingredient of understanding superfluid turbulence, a phenomenon recently also reported in trapped atomic Bose-Einstein condensates. In this work we show that, despite the established dependence of vortex motion on temperature in such systems, vortex reconnections are actually temperature independent on the typical length/time scales of atomic condensates. Our work is based on a dissipative Gross-Pitaevskii equation for the condensate, coupled to a semiclassical Boltzmann equation for the thermal cloud (the Zaremba-Nikuni-Griffin formalism). Comparison to vortex reconnections in homogeneous condensates further show reconnections to be insensitive to the inhomogeneity in the background density.Comment: 6 pages, 4 figure

Reliability of the time splitting Fourier method for singular solutions in quantum fluids

We study the numerical accuracy of the well-known time splitting Fourier spectral method for the approximation of singular solutions of the Gross\u2013Pitaevskii equation. In particular, we explore its capability of preserving a steady-state vortex solution, whose density profile is approximated by an accurate diagonal Pad\ue9 expansion of degree [8,8], here explicitly derived for the first time. We show by several numerical experiments that the Fourier spectral method is only slightly more accurate than a time splitting finite difference scheme, while being reliable and efficient. Moreover, we notice that, at a post-processing stage, it allows an accurate evaluation of the solution outside grid points, thus becoming particularly appealing for applications where high resolution is needed, such as in the study of quantum vortex interactions

Stabilization of Tollmien-Schlichting Waves by Mode Interaction

Decreasing skin friction in boundary layers attached to aircraft wings can have an impact in both fuel consumption and pollutant production, which are becoming crucial to reduce operation costs and meet environmental regulations, respectively. Skin friction in turbulent boundary layers is about ten times that of laminar boundary layers. Thus, an obvious method to reduce friction drag is to delay transition to turbulence, which is a fairly involved process in real aircraft wings [J98]. Transition sis promoted either by Tollmien—Schlichting (TS) and Klebanov (K) modes [K94], with the former playing an essential role. Various methods (e.g., suction [SG00,ZLB04], wave cancellation [WAA01,LG06]) have been proposed to reduce TS modes in laminar boundary layers. Mode interaction methods have been successfully used in fluid systems to control related instabilities, such as the Rayleigh—Taylor instability [LMV01]. Here, we present some recent results on using these methods to control TS modes in a compressible, 2D boundary layer over a flat plate at zero incidence. A given unstable TS mode can be stabilized by coupling its spatial evolution with that of a second selected stable TS mode, in such a way that the stable mode takes energy from the unstable one and gives a stable coupled evolution of both modes. The coupling device is a wavetrain in the boundary layer, with appropriate wavenumber and frequency, which can be created by an array of oscillators on the wall, and promotes both (i) parametric coupling between the stable and unstable TS modes and (ii) a mean flow that is also stabilizing. Three differences with wave cancelation methods are relevant. Namely, (a) nonlinear terms play an essential role in the process; (b) the unstable TS mode is stabilized (its growth rate is decreased), not just canceled; and (c) stabilization does not depend on the phase of the incoming wave, which implies that active control is not necessary

Helicity within the vortex filament model

Kinetic helicity is one of the invariants of the Euler equations that is associated with the topology of vortex lines within the fluid. In superfluids, the vorticity is concentrated along vortex filaments. In this setting, helicity would be expected to acquire its simplest form. However, the lack of a core structure for vortex filaments appears to result in a helicity that does not retain its key attribute as a quadratic invariant. By defining a spanwise vector to the vortex through the use of a Seifert framing, we are able to introduce twist and henceforth recover the key properties of helicity. We present several examples for calculating internal twist to illustrate why the centreline helicity alone will lead to ambiguous results if a twist contribution is not introduced. Our choice of the spanwise vector can be expressed in terms of the tangential component of velocity along the filament. Since the tangential velocity does not alter the configuration of the vortex at later times, we are able to recover a similar equation for the internal twist angle to that of classical vortex tubes. Our results allow us to explain how a quasi-classical limit of helicity emerges from helicity considerations for individual superfluid vortex filaments

"Delirium Day": A nationwide point prevalence study of delirium in older hospitalized patients using an easy standardized diagnostic tool

Background: To date, delirium prevalence in adult acute hospital populations has been estimated generally from pooled findings of single-center studies and/or among specific patient populations. Furthermore, the number of participants in these studies has not exceeded a few hundred. To overcome these limitations, we have determined, in a multicenter study, the prevalence of delirium over a single day among a large population of patients admitted to acute and rehabilitation hospital wards in Italy. Methods: This is a point prevalence study (called "Delirium Day") including 1867 older patients (aged 65 years or more) across 108 acute and 12 rehabilitation wards in Italian hospitals. Delirium was assessed on the same day in all patients using the 4AT, a validated and briefly administered tool which does not require training. We also collected data regarding motoric subtypes of delirium, functional and nutritional status, dementia, comorbidity, medications, feeding tubes, peripheral venous and urinary catheters, and physical restraints. Results: The mean sample age was 82.0 \ub1 7.5 years (58 % female). Overall, 429 patients (22.9 %) had delirium. Hypoactive was the commonest subtype (132/344 patients, 38.5 %), followed by mixed, hyperactive, and nonmotoric delirium. The prevalence was highest in Neurology (28.5 %) and Geriatrics (24.7 %), lowest in Rehabilitation (14.0 %), and intermediate in Orthopedic (20.6 %) and Internal Medicine wards (21.4 %). In a multivariable logistic regression, age (odds ratio [OR] 1.03, 95 % confidence interval [CI] 1.01-1.05), Activities of Daily Living dependence (OR 1.19, 95 % CI 1.12-1.27), dementia (OR 3.25, 95 % CI 2.41-4.38), malnutrition (OR 2.01, 95 % CI 1.29-3.14), and use of antipsychotics (OR 2.03, 95 % CI 1.45-2.82), feeding tubes (OR 2.51, 95 % CI 1.11-5.66), peripheral venous catheters (OR 1.41, 95 % CI 1.06-1.87), urinary catheters (OR 1.73, 95 % CI 1.30-2.29), and physical restraints (OR 1.84, 95 % CI 1.40-2.40) were associated with delirium. Admission to Neurology wards was also associated with delirium (OR 2.00, 95 % CI 1.29-3.14), while admission to other settings was not. Conclusions: Delirium occurred in more than one out of five patients in acute and rehabilitation hospital wards. Prevalence was highest in Neurology and lowest in Rehabilitation divisions. The "Delirium Day" project might become a useful method to assess delirium across hospital settings and a benchmarking platform for future surveys

Nonlinear optimal perturbations in a Couette flow: bursting and transition

This paper provides the analysis of bursting and transition to turbulence in a Couette flow, based on the growth of nonlinear optimal disturbances. We use a global variational procedure to identify such optimal disturbances, defined as those initial perturbations yielding the largest energy growth at a given target time, for given Reynolds number and initial energy. The nonlinear optimal disturbances are found to be characterized by a basic structure, composed of inclined streamwise vortices along localized regions of low and high momentum. This basic structure closely recalls that found in boundary-layer flow (Cherubini et al., J. Fluid Mech., vol. 689, 2011, pp. 221–253), indicating that this structure may be considered the most ‘energetic’ one at short target times. However, small differences in the shape of these optimal perturbations, due to different levels of the initial energy or target time assigned in the optimization process, may produce remarkable differences in their evolution towards turbulence. In particular, direct numerical simulations have shown that optimal disturbances obtained for large initial energies and target times induce bursting events, whereas for lower values of these parameters the flow is directly attracted towards the turbulent state. For this reason, the optimal disturbances have been classified into two classes, the highly dissipative and the short-path perturbations. Both classes lead the flow to turbulence, skipping the phases of streak formation and secondary instability which are typical of the classical transition scenario for shear flows. The dynamics of this transition scenario exploits three main features of the nonlinear optimal disturbances: (i) the large initial value of the streamwise velocity component; (ii) the streamwise dependence of the disturbance; (iii) the presence of initial inclined streamwise vortices. The short-path perturbations are found to spend a considerable amount of time in the vicinity of the edge state (Schneider et al., Phys. Rev. E, vol. 78, 2008, 037301), whereas the highly dissipative optimal disturbances pass closer to the edge, but they are rapidly repelled away from it, leading the flow to high values of the dissipation rate. After this dissipation peak, the trajectories do not lead towards the turbulent attractor, but they spend some time in the vicinity of an unstable periodic orbit (UPO). This behaviour led us to conjecture that bursting events can be obtained not only as homoclinic orbits approaching the UPO, as recently found by van Veen & Kawahara (Phys. Rev. Lett., vol. 107, 2011, p. 114501), but also as heteroclinic orbits between the equilibrium solution on the edge and the UPO

The minimal seed of turbulent transition in the boundary layer

This paper describes a scenario of transition from laminar to turbulent flow in a spatially developing boundary layer over a flat plate. The base flow is the Blasius non-parallel flow solution; it is perturbed by optimal disturbances yielding the largest energy growth over a short time interval. Such perturbations are computed by a nonlinear global optimization approach based on a Lagrange multiplier technique. The results show that nonlinear optimal perturbations are characterized by a localized basic building block, called the minimal seed, defined as the smallest flow structure which maximizes the energy growth over short times. It is formed by vortices inclined in the streamwise direction surrounding a region of intense streamwise disturbance velocity. Such a basic structure appears to be a robust feature of the base flow since it is practically invariant with respect to the initial energy of the perturbation, the target time, the Reynolds number and the dimensions of the computational domain. The minimal seed grows very rapidly in time while spreading, and it triggers nonlinear effects which bring the flow to turbulence in a very efficient manner, through the formation of a turbulence spot. This evolution of the initial optimal disturbance has been studied in detail by direct numerical simulations. Using a perturbative formulation of the Navier–Stokes equations, each linear and nonlinear convective term of the equations has been analysed. The results show the fundamental role of the streamwise inclination of the vortices in the process. The nonlinear coupling of the finite amplitude disturbances is crucial to sustain such streamwise inclination, as well as to generate dislocations within the flow structures, and local inflectional velocity distributions. The analysis provides a picture of the transition process characterized by a sequence of structures appearing successively in the flow, namely, 3 vortices, hairpin vortices and streamwise streaks. Finally, a disturbance regeneration cycle is conceived, initiated by the fast nonlinear amplification of the minimal seed, providing a possible scenario for the continuous regeneration of the same fundamental flow structures at smaller space and time scales